Science and Technology Journal of BgNS, VOL. 13, No. 1, JUNE 2009
ISSN 1310-8727
Title:
AN EQUATION OF MOTION APPROACH TO MULTIPHONON
NUCLEAR SPECTRA
Authors:
F. Adreozzi, F. Knapp, N. Lo Ludice, A. Porrino, and J.Kavasil
Abstract:
A method developed recently for treating exactly multiphonon excitations in
nuclei is outlined . It consists in constructing equations of motion within a subspace
spanned by states which are tensor products of Tamm Dancoff phonons. Recursive
formulas allow to solve these equations iteratively, thereby generating a basis of
microscopic multiphonon states. The basis states so obtained make sparse the Hamiltonian
matrix, which is, then, easily diagonalized. A numerical application on 16O show how the
implementation of the method can be carried out with no approximations.
References
[1] D.J. Rowe, Nuclear Collective Motion (Methuen London, 1970).
[2] P.Ring and P.Scuck, The Nuclear Meny/Body Problem (Springer-Verlag New York,
1980).
[3] P.F.Bortignon, A.Bracco, and R.A.Brogila, Giant Resonances (Harwood academic
publishers, Amsterdam, 1998).
[4] M.Kneissl, H.H. Pitz and A.Zilger, Prog. Part. Nucl. Phys. 37 (1996) 439.
[5] N.Pietrala et al., Phys. Rev. Lett. 83 (1999) 1303.
[6] C. Fransen et al., Phys. Rev. C 71 (2005) 054304
[7] M.Kneissl, N.Pietrala, and A.Zilger, J. Phys. G: Nucl. Part. Phys. 32 (2006) R217.
[8] N. Lo Ludice, and F. Palumbo, Phys. Rev. Lett. 41 1532 (1978).
[9] D. Bohle, A.Richter, W. Steffen, A.E. Dieperink, N. Lo Ludice, F. Palumbo, and
O.Sholten, Phys. Lett B 137 (1984).
[10] M.Kricka, F.Becvar, J. Honzatko, I.Tomandl, M.Heil, E.Kappeler, R. Reifarth,
F.Voss, K.Wisshak, Phys. Rev. Lett. 92 17250 (2004).
[11] S.R.Lesher et al., Phys. Rev. C 66, 051305R (2002).
[12] H.F.Wirth et al. Phys. Rev. C 69, 0443105 (2004).
[13] D.Bucurescu et al., Phys. Rev. C 73, 064309 (2006).
[14] D.A.Meyer et al., J. Phys. G: Nucl. Part. Phys. 31, S 1399 (2005).
[15] D.A.Meyer et al., Phys. Lett. B638, 44 (2006].
[16] D.A.Meyer et al., Phys. Rev. C 74, 044309 (2006).
[17] N.Frascaria, Nucl. Phys. A 482 (1988) 245 c.
[18] T.Auman, P.F. Bortignon, H.Hemling, Annu. Rev. Nucl. Part. Sci. 48 (1998) 351.
[19] C.A.Bertulani and V.Yu. Ponomarev, Phys. Rep. 32 (1999) 139.
[20] For a review see A.Arima and F.Iachello, Adv. Nucl. Phys. 13 (1984) 139.
[21] S.T.Belyaev and V.G.Zalevinsky, Nucl. Phys. 39 (1962) 582.
[22] T.Marumori, M.Yamamura, and A.Tokunaga, Progr. Thor. Phys. 31 (1964) 1009.
[23] For a review see A. Klein and E.R. Marshalek, Rev. Mod. Phys. 63 (1991) 375.
[24] T.Otsuka, A.Arinma and F.Iachello, Nucl. Phys. 309 (1978).
[25] See also for references A.Bohr and B.R. Mottelson, Nuclear Structure, vol. II
(Benjamin, New York, 1975).
[26] See also for references P.F.Bortignon, R.A.Broglia, D.R. Bes and R. Liotta, Phys.
Rep. 30 (1977) 305.
[27] V.G.Soloviev, Theory of Atomic Nuclei; Quasiparticles and Phonons (Institute of
Physics, Bristol, 1992).
[28] N. Lo Ludice and Ch.Stoyanov, Phys. Rev. C 62 (2000) 047302; Phys. Rev. C 65
(2002) 064304.
[29] V.Yu. Ponomarev, P.F.Bortignon, R.A.Broglia, and V.V.Voronov, Phys. Rev. Lett.
(2000) 85 1400.
[30] C.Pomar, J. Blomqvist, R.J.Liota and A.Insolia, Nucl. Phys. A 515 (1990) 381.
[31] M.Grinberg, R.Piepenbring, K.V.Protasov, B.Silvestre-Brac, Nucl. Phys. A 597
(1996) 355.
[32] F. Adreozzi, N. Lo Ludice, and A.Porrino, F.Knapp, J.Kvasil, Phys. Rev. C 75
044312 (2007)
[33] N. Lo Ludice, A.V.Sushkov, and N.Yu.Shirikova, Phys. Rev. C 70 064316 (2004).
[34] N. Lo Ludice, A.V.Sushkov, and N.Yu.Shirikova, Phys. Rev. C 72 034303 (2005).
[35] D.J.Rowe, J.Math. Phys. 10 (1969) 1774.
[36] R.J.Liota and C.Pomar, Nucl. Phys. (1982) A382 1.
[37] K.V.Protasov, B.Silvestre-Brac, R.Piepenbring, and M.Grinberg Phys. Rev. C 53
(1996) 1646.
[38] G.E.Brown, A.M. Green, Nucl. Phys. 75 (1966) 401.
[39] W.C. Haxton and C.J. Johnson, Phys. Rev. Lett.65 (1990) 1325.
[40] T.Dytrich, K.D.Sviratcheva, C,Bahri, J.P.Draayer, J.P.Vari, Phys. Rev. Lett. 98,
162503 (2007).
[41] P.Ring and P.Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New
York, (1980).
[42] R.Machleidt, Adv. Nucl. Phys. 19 (1989) 189.
[43] F. Palumbo, Nucl. Phys. 99 (1967) 100.
[44] D.H.Glockner and R.D. Lawson, Phys. Lett. B 53 (1974) 313.
[45] D.R.Tilley, H.R.Weller and C.M. Cheves, Nucl. Phys. A564 (1993).
[46] D.L.Berman and S.C.Filtz, Rev Mod. Phys. 47 (1975) 713.
[47] Y.W.Lui, H.L.Clark and D.H. Youngblood, Phys. Rev. C 64 (2001) 064308.
[48] See for instance J.Kvasil, N. Lo Ludice, V.O. Nesterenko, and M.Kopal, Phys. Rev.
C 58 (1998) 209.